Apparently, there's a trend in the western media, as well as among some professing Christians, to refer to Muhammad as "The Prophet Muhammad" or simply "The Prophet." I say "apparently" because I don't read, watch, or listen to these people, so my information is admittedly secondhand.
There are several issues here:
i) Some people defend it on the grounds that so many Muslims are named Muhammad that you need some additional descriptor to distinguish the founder of Islam from his many namesakes.
ii) Some people defend this honorific usage on the grounds of politeness.
iii) Apropos (ii), some people say we should avoid giving unnecessary offense.
Let's run back through these:
i) The problem with (i) is that some proper names and place-names have a default referent. The very lack of further descriptors means they denote the most famous referent.
ii) In addition, the context often determines the referent. If I'm reading a commentary on Romans, "Paul" denotes the Apostle Paul. That's understood.
iii) Apropos (i), it depends on where we enter a discussion. If this is an ongoing discussion which someone else started, the identity of the referent may be a given. That was established at the outset.
If a Christian initiates the discussion, he might use a descriptor like "the founder of Islam" to establish the referent. But you don't need to repeat the identification throughout the conversation. Having established the identity of the referent, thereafter you can simply say "Muhammad."
Or, the identity of the referent might be implicit from something related to Muhammad, like the origin of the Koran.
iv) There's a difference between deliberate offense and gratuitous offense. I agree that Christians should avoid giving unnecessary offense, but sometimes it's necessary or simply unavoidable to give offense.
What doesn't offend Muslims? Muslims are offended by the existence of anyone who is not Muslim. If you're not Muslim, you're an infidel. First and foremost–it's not what you say or do, but what you are, that's intolerable. You could say nothing, or you could mouth all the right honorific titles, but that's insufficient to placate Muslim sensibilities.
For that matter, it's not enough to be Muslim. It's offensive to be the wrong kind of Muslim. Sunnis are offensive to Shiites, and vice versa.
v) Apropos (iv), it's not enough to say "the Prophet Muhammad" or "the Prophet." You're supposed to add "Peace be upon him" every time you say or hear his name.
vi) Apropos (iv), Muhammad is a paradigm false prophet. He's typecast for how the OT defines a false prophet. And he's the most influential false prophet in history.
Muslims need to understand how Christians view Muhammad. And they need to understand why we view him that way.
Some people have beliefs that are dangerously out of touch with reality. In that event, you can't avoid offending them if we tell them what they need to hear.
vii) Whenever we defer to Muslim sensibilities, we empower them. We embolden them. We cede power to them. We give them power over the rest of us. That's power they will use and abuse.